Kendall correlation

Description

The Kendall Tau Rank Correlation Coefficient is used to measure the
degree of correspondence between sets of rankings where the measures are not
equidistant. It is used with
non-parametric data

The Kendall coefficient
is denoted with the Greek letter tau (τ).

τ = (4P / (n * (n - 1))) - 1

Where P is the number of concordant pairs
and is calculated as the sum over all the items, of items ranked after the given
item by both rankings.

Example

A group of people, denoted as A to E, have their IQ and hat size measured, to
determine if a bigger brain makes you brainier. The people are ranked by both IQ
and hat size (1 - highest rank), and put in a table, as below.

Person

A

B

C

D

E

Rank by IQ

1

2

3

4

5

Rank by hat size

3

5

2

1

4

Number of higher
ranked hat sizes
(lower numbers)
to the right

2

3

1

0

0

Now P is the sum of the 'unexpected' rankings, measured as the sum of the
number ranked hat sizes to the right (ie. in lower positions than the assessed
position).